An International Conference on: New Challenges and Perspectives in Symplectic Field Theory

“辛场论的新挑战和新观点”国际会议将于2007年6月25日至29日在斯坦福大学举行。这将是在这一主题上举行的第一次如此大规模的会议。会议将接待世界领先的数学家，其中包括著名的高级研究人员(Donaldson、Eliashberg、Fukaya、Gabai、Givental、Gromov、Hitchin、Hofer、McDuff、Witten等)，但重点肯定是优秀的年轻数学家和一些处于生产力顶峰的中年数学家。SFT研究具有接触边界的辛流形上的代数不变量。它既捕捉到辛流形内部的几何(通过Gromov-Witten不变量的推广)，又捕捉到接触边界分量的Reeb轨道的精细几何。它在一个单一的框架中包括SFT的祖先，即辛同调和联络同调。这次会议将在SFT和其他迅速发展的密集数学研究学科开始以最令人兴奋和最有希望的方式相互作用的关键时刻举行。特别是与新的低维拓扑不变量，如Oszvath和Szabo的拓扑不变量的关系，以及与新的Floer理论发展(如分枝Floer同调或簇复合体)的关系，以及与可积系统的谱系的关系。外科、正则性和紧致性问题将被讨论，在纽结理论、动力系统、拉格朗日嵌入的拓扑中的各种应用也将是来自不同背景的专家交互的焦点。‘辛场理论的新挑战和前景’国际会议将于2007年6月25-29日在斯坦福大学举行。这将是在这一主题上举行的第一次如此大规模的会议。会议将接待世界领先的数学家，其中包括久负盛名的资深研究人员，但明确的重点是优秀的年轻数学家和一些处于生产力顶峰的中年数学家。SFT处理的问题是，在一个强大的框架内，将发生动力系统的环境空间的“内部拓扑”的几何与这些系统闭合轨道的复杂行为结合起来。它的最终目的是了解环境空间的拓扑在多大程度上决定了动力学定律的定性行为。它提出了许多深刻的、绝对令人着迷的分析和代数挑战，并与世界上许多迅速崛起的科学研究领域有关，例如最近在低维拓扑学(3维和4维)或被物理学家称为“可积系统和层次”的对象的结构方面的发展，这些结构在过去50年里一直是一个复兴的研究主题。

The international Conference on ``New Challenges and Perspectives in Symplectic Field Theory (SFT)'' will take place at Stanford University, June 25--29, 2007. This will be the very first conference of such amplitute to be held in this subject. The Conference will host the world's leading mathematicians including the well established senior researchers (Donaldson, Eliashberg, Fukaya, Gabai, Givental, Gromov, Hitchin, Hofer, McDuff, Witten, ...), but with a definite focus on strong younger mathematicians and some mid-carreer mathematicians at the peak of their productivity. SFT deals with algebraic invariants attached to symplectic manifolds with contact boundaries. It captures both the geometry of the interior of the symplectic manifold (through a generalization of the Gromov- Witten invariants) and the subtle geometry of the Reeb orbits of the contact boundaries components. It includes, in a single framework, the ancestors of SFT, i.e the symplectic and contact homologies. The Conference will happen at a crucial moment when SFT and other rapidly growing subjects of intensive research in mathematics have begun to interact in the most exciting and promising way. In particular, the relations with new low dimensional topological invariants, eg those of Oszvath and Szabo, as well as with new Floer theoretical developments (eg the Branching Floer Homology or the Cluster complexes) and with hierarchies of integrable systems will be explored. Surgery, regularity and compactness problems will be discussed and various applications to knot theory, dynamical systems, the topology of Lagrangian embeddings will also be the focus of interactions amongst specialists of diverse backgrounds.The international conference on ``New Challenges and Perspectives in Symplectic Field Theory (SFT)'' will take place at Stanford University, June 25--29, 2007. This will be the very first conference of such amplitute to be held in this subject. The Conference will host the world's leading mathematicians including the well established senior researchers but with a definite focus on strong younger mathematicians and some mid-carreer mathematicians at the peak of their productivity. SFT deals with the problem of integrating, in a single powerful framework, the geometry of the ``internal topology'' of ambient spaces where dynamical systems occur, with the intricate behaviour of closed orbits of these systems. Its ultimate aim is to understand to which extent the topology of ambient spaces determines the qualitative behaviour of dynamical laws. It poses lots of deep, absolutely fascinating analytical and algebraic challenges and bears relations to many rapidly emerging fields of scientific investigation in the world, like the recent development in low dimensional topology (in dimension 3 and 4) or the structure of objects known to physicists as ``integrable systems and hierarchies'' that have been a resurgent theme of research over the last fifty years.